Big-bang nucleosynthesis: A probe of the early Universe

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 611 (2009) 224–230

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Big-bang nucleosynthesis: A probe of the early Universe Alain Coc Centre de Spectrome trie Nucle aire et de Spectrome trie de Masse (CSNSM), CNRS/IN2P3, Universite Paris Sud, UMR 8609, Bˆ atiment 104, F–91405 Orsay Campus, France

a r t i c l e in f o

a b s t r a c t

Available online 5 August 2009

Primordial nucleosynthesis is one of the three observational evidences for the Big-Bang model. Even though they span a range of nine orders of magnitude, there is indeed a good overall agreement between primordial abundances of 4 He, D, 3 He and 7 He either deduced from observation or primordial nucleosynthesis. This comparison was used for the determination of the baryonic density of the Universe. For this purpose, it is now superseded by the analysis of the Cosmic Microwave Background radiation anisotropies. Big-Bang nucleosynthesis remains, nevertheless, a valuable tool to probe the physics of the early Universe. & 2009 Elsevier B.V. All rights reserved.

Keywords: Big-Bang nucleosynthesis Primordial abundances

1. Introduction There are presently three observational evidences for the BigBang model: the universal expansion, the Cosmic Microwave Background (CMB) radiation and Primordial or Big-Bang Nucleosynthesis (BBN). The Hubble law states that the recession velocity of a galaxy is proportional to its distance: Vrec ¼ H0  D where H0 is the Hubble constant. (It is usual to parametrize H0 as H0 ¼ h  100 km=s=Mpc with h  73 [1].) It is a direct consequence of the expansion of the Universe assuming that spatial dimensions are all proportional to a scale factor aðtÞ that increases with time. Wavelengths are also affected by the expansion, lpaðtÞ, so that the redshift z is given by z  l0 =l  1 ¼ a0 =a  1

ð1Þ

where a ðlÞ and a0 ðl0 Þ are the scale factors (wavelengths), respectively at emission and present times.1 Recombination of the free electrons with protons occurs when the temperature drops below 3000 K. Space, now filled with neutral atoms, becomes transparent for the first time and thermalized photons are free to roam the Universe. Because of the expansion, photons are affected by redshift so that their present temperature has now dropped to  2:725 K bringing this radiation into the microwave domain. The third evidence for a hot Big-Bang comes from the primordial abundances of the ‘‘light elements’’: 4 He, D, 3 He and 7 He. They are produced during the first  20 min of the Universe when it was dense and hot enough for nuclear reactions to take place. These primordial abundances can, in principle, be deduced from astronomical observations of objects that were formed E-mail address: [email protected] Present values are usually labeled with index 0.

1

0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.07.052

shortly after the Big-Bang. When compared with BBN calculations, the overall agreement spans nine orders of magnitudes. BBN used to be the only method to determine the baryonic content of the Universe. The number of free parameters entering Standard BBN have decreased with time. The number of light neutrino families is known from the measurement of the Z 0 width by LEP experiments at CERN: Nn ¼ 2:984070:0082 [2]. The lifetime of the neutron (entering in weak reaction rate calculations) and the nuclear reaction rates have been measured in nuclear physics laboratories. The last parameter to have been independently determined is the baryonic density of the Universe which is now deduced from the observations of the anisotropies of the CMB radiation. When considering density components of the Universe, it is convenient to refer to the critical density which corresponds to a flat 3D-space. It is given by

r0;C ¼

3H02 ¼ 1:88h2  1029 g=cm3 8pG

ð2Þ

where G is the gravitational constant. It corresponds to a density of a few hydrogen atoms per cubic meter or one typical galaxy per cubic megaparsec. Densities are now given relative to r0;C with the notation O  r=r0;C . Table 1 gives the principal components to the density of the Universe. The total density is very close to the critical density but is dominated by vacuum energy and dark matter contributions. The baryonic matter only amounts to  4% of the total density or 17% of the total matter content. What we observe with our telescopes corresponds to only 103 of the total. Is is usual to introduce Z, the number of photons per baryon which remains constant during the expansion and is directly related to Ob by Ob  h2 ¼ 3:65  107 Z with Ob  h2 ¼ 0:02230þ0:00075 (‘‘WMAP 0:00073 only’’ [3]).

ARTICLE IN PRESS A. Coc / Nuclear Instruments and Methods in Physics Research A 611 (2009) 224–230

Table 1 Density components of the Universe, adapted from Ref. [1]. Radiation (CMB) energy

ORðCMBÞ

 5  105

Visible matter Baryonic matter Matter (darkþbaryonic) Vacuum energy

OL Ob OM OL

 0:003  0:04  0:3  0:7

Total

OT

1

225

which represents the Cosmological Principle: homogeneity and isotropy of the Universe. aðtÞ is the above-mentioned scale factor and k ¼ 0 or 71 marks the absence or sign of space curvature. In an appropriate (free falling) referential, the energy–momentum tensor has only non-zero diagonal elements: ðr; p; p; pÞ where r and p are the energy density and pressure of the fluid. It leads to the Friedmann equation that links the rate of expansion to the energy density r: rffiffiffiffiffiffiffiffiffiffiffiffiffi 1 da 8pGr HðzÞ  ¼ H0 O1=2 ðzÞ ð4Þ ¼ 3 a dt with (Eq. (2)),

η = ηWMAP

OðzÞ  OM ðz þ 1Þ3 þ OR ðz þ 1Þ4 þ OL þ ð1  OT Þðz þ 1Þ2

Given the values from Table 1, at BBN when z108 , the dominant term is the ‘‘radiation’’ term, OR . This corresponds to all the relativistic particles whose energies also scale as a1 in addition to the a3 number density factor. The important consequence is that during BBN, HðtÞ is only governed by relativistic particles while the baryons, cold dark matter, cosmological constant or curvature terms play no role (Eq. (5)). The radiation density for species i, rR;i , is given by the Stefan– Boltzmann law:

A

1 Neutrons mass fraction

B

10-1

rR;i ¼ gi 10-2

10-3 109

1010 Temperature (K)

1011

1012

Fig. 1. Neutron mass fraction as a function of temperature. The curves represent the n2p equilibrium (dashed line), the free neutron decay (dash-dotted line) and the full network calculation (solid line).

2. Physics of the expanding Universe in the BBN era At temperatures slightly above 1010 K, the particles present are: photons, electrons, positrons, the three families of neutrinos and antineutrinos, plus a few neutrons and protons. All these particles are in thermal equilibrium so that the numbers of neutrons and protons are simply related (Fig. 1) by Nn =Np ¼ expðQnp =kB TÞ where Qnp ¼ 1:29 MeV is the neutron–proton mass difference. This holds until T  1010 K, when the n2p reactions (ne þ n2e þ p and n e þ p2eþ þ n) become slower than the rate of expansion HðtÞ (label ‘‘A’’ in Fig. 1). Afterwards, the ratio at freezeout Nn =Np  0:2 slightly decreases due to free neutron beta decay until the temperature is low enough ðT  109 KÞ for the first nuclear reaction n þ p-D þ g to become faster than the reverse photodisintegration ðD þ g-n þ pÞ that up to now prevented the production of heavier nuclei (label ‘‘B’’ in Fig. 1). From that point on, the remaining neutrons almost entirely end up bound in 4 He while only traces of D, 3 He and 7 Li are produced. The 4 He yield is directly related to the Nn =Np ratio at freezeout occurring if the expansion rate HðtÞ is comparable to the weak rates. HðtÞ is obtained from the Einstein equation that links the curvature and energy–momentum tensors. The first one is derived from the metrics (Friedmann–Lemaıˆtre–Robertson–Walker), ds2 ¼ dt 2  a2 ðtÞ



dr 2

1  kr

2

ð5Þ

2

þ r2 ðdy þ sinydf Þ 2

 ð3Þ

k2B p2 30‘

3

Ti4 

gi aR Ti4 2

ðbosonsÞ

ð6Þ

where gi is the spin factor and aR the radiation constant. For fermions (e.g. electrons), an additional factor of 78 must be inserted. In the radiation dominated era, in particular during BBN, the expansion rate is hence simply given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8pGaR geff ðTÞ H¼ ð7Þ  T 2: 6 The effective spin factor geff ðTÞ includes contributions from photons ðgg  2Þ, neutrinos (gn ¼ 2  Nn 78 ðTn =Tg Þ4 as Tn aTg  T, with Nn ¼ 3 the number of neutrino families) and electrons/ positrons (from 2  2  78 for Tbme to 0 for T5me ). When particles annihilate the released energy is shared among the other particles they were in equilibrium with. As neutrinos decouple from other particles before electron–positron annihilation they do not take advantage of the corresponding reheating.

3. Primordial abundances During the evolution of the Galaxy, nucleosynthesis takes place mainly in massive stars which release matter enriched in heavy elements into the interstellar medium when they explode as supernovae. Accordingly, the abundance of heavy elements in the gas, at the origin of star formation, increases with time. The observed abundance of metals2 is hence an indication of its age: the older the lower the metallicity. Primordial abundances are hence extracted from observations of objects which are thought to be the most primitive followed by an extrapolation to zero metallicity. Fig. 2 shows observations of lithium, beryllium and boron at the surface of low metallicity stars found in the halo of our galaxy. The abundances of beryllium and boron increase with metallicity (i.e. with time) confirming that these elements are continuously 2 In astrophysics, metals means all elements with Z42 and the abundance of metals is called metallicity. Logarithm of metallicity relative to solar ðÞ is often used with the notation ½X=H ¼ logðX=HÞ  logðX =H Þ where X is usually Fe. Hence, for instance, ½Fe=H ¼ 0 or 3 correspond to a solar, or 103 solar metallicity.

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-8

4He

primordial abundance

0.3 0.29 0.28

-10

0.27

-11

Protosolar

0.26 Yp

log (N(Li, Be,B)/N(H))

-9

-12 -13

0.24

Li B Be

-14

0.25 0.23 0.22 0.21

-15 -4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

[Fe/H] Fig. 2. Observed lithium, beryllium and boron abundances in halo stars as a function of logarithm of metallicity (see footnote and references in Ref. [4]).

D/H

10-4

Mean (2σ)

10-5 -3.5

-3

-2.5

-2

-1.5

-1

-0.5

[O/H] (or [Si/H]) Fig. 3. Recent deuterium observations in cosmological clouds as a function of logarithm of metallicity (see references in Ref. [7]).

synthesized.3 On the contrary, for ½Fe=H o  1:3 the abundance of lithium is independent of metallicity, displaying a plateau. This constant Li abundance was interpreted [5] as corresponding to the BBN 7 Li yield. This interpretation assumes that lithium has not been depleted at the surface of these stars so that the presently observed abundance is equal to the initial one. The presence of the ‘‘Spite plateau’’ is an indication that depletion may not have been very effective. On the contrary, younger stars ð½Fe=H 4  1Þ display a large dispersion in lithium abundances reflecting the effects of different production and destruction mechanisms. Recent observations [6] have led to a relative primordial 10 (95% c.l.) obtained by abundance of Li=H ¼ ð1:23þ0:68 0:32 Þ  10 extrapolation to zero metallicity ðFe=H ¼ 0Þ. Contrary to 7 Li which can be both produced (spallation, asymptotic giant branch (AGB) stars, novae) and destroyed (in the interior of stars), deuterium, a very fragile isotope, can only be destroyed after BBN, in particular at the very first stage of star formation. Its primordial abundance has thus to be determined from the observation of cold objects. Clouds at high redshift on the line of sight of even more distant quasars are thought to be the

3 Be, B, 6 Li and some 7 Li are produced by a spallation process: mainly breaking C, N and O nuclei by p and a at high energy in the interstellar medium [4].

0.2 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Year Fig. 4. Recent determination of 4 He primordial abundances, ordered by publication date [8–13]. Dashed lines and arrow represent our adopted limits [9].

best candidates. Absorption line observations enable the determination of the D=H ratio. Unfortunately, there are few good candidates (half a dozen) and there is no evidence of a plateau nor of a tendency that could be extrapolated to zero metallicity (Fig. 3). The adopted primordial D abundance is hence given by 5 of D=H observations in these the average value ð2:78þ0:44 0:38 Þ  10 cosmological clouds [7]. After BBN, 4 He is only produced by stars. Its primordial abundance is deduced from observations in HII (ionized hydrogen) regions of compact blue galaxies. Galaxies are thought to be formed by the agglomeration of such dwarf galaxies which are hence considered as more primitive. The primordial 4 He abundance Yp (4 He mass fraction) is given by the extrapolation to zero metallicity [8–13]. It is affected by systematic uncertainties [9,11] such as plasma temperature or stellar absorption. In Fig. 4 the range of Yp values is depicted according to different authors as gathered in Ref. [8] and completed by Refs. [10–13] values. As the most recent determinations, based on almost the same set of observations, but different atomic physics, lead to a large scatter of values, here, we will use a safe interval, 0:232oYp o0:258 [9], to account for systematic uncertainties. Contrary to 4 He, 3 He is both produced and destroyed in stars so that the evolution of its abundance as a function of time is not well known. Because of the difficulties of helium observations and the small 3 He=4 He ratio, 3 He has only been observed in our galaxy. The 3 He abundances observed in galactic HII regions display a plateau as a function of the galactic radius and in a limited range of metallicities: 0:6o½Fe=H o0:1 [14]. It is, however, difficult to extrapolate this galactic value (spanning only a limited range of Fe=H) to zero metallicity so that 3 He is usually not used to constrain BBN. An upper limit on 3 He primordial abundance is given by [14]: 3 He=H ¼ ð1:170:2Þ 105 , based on their best observed source.

4. Nuclear reactions Unlike in other sectors of nuclear astrophysics, nuclear crosssections have usually been directly measured at BBN energies ð100 keVÞ. Fig. 5 shows the 12 nuclear reactions responsible for the production of 4 He, D, 3 He and 7 He in Standard BBN. Note the presence of the radioactive tritium ð3 HeÞ and 7 Be that will later decay into 3 He and 7 Li, respectively. There are many other

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227

n+p → d+γ 7Be

σM1+E1 (mb)

H

ig

h

Ω

B

0.3

1H

2

H

4

He

(d,γ) (d,n) (p,γ)

3H

X

(α,γ)

(p,α) (n,p) n

0.1

0.3

(n,γ) (d,p)

0.2

0

σM1 (mb)

3He

Lo

w

Ω

B

7Li

0.2

0.1 Fig. 5. The 12 BBN main reactions for the productions of 4 He, D, 3 He and 7 He, showing the low ðZt3  1010 Þ and high ðZ\3  1010 Þ baryonic density branches 7 for the Li synthesis.

0 1

reactions connecting these isotopes, but their cross-sections are too small and/or reactants too scarce to have any significant effect. The weak reactions involved in n2p equilibrium are an exception; their rates [15] come from the standard theory of the weak interaction normalized to the experimental neutron lifetime: 885:770:8 s [1]. (See this conference proceedings for a discussion of neutron lifetime.) The n þ p-D þ g reaction rate is also obtained from theory [16] but in the framework of Effective Field Theory. Few experimental data are available at BBN energies but they all confirm the theoretical results (Fig. 6). For the 10 remaining reactions, 2 Hðp; gÞ3 He, 2 Hðd; nÞ3 He, 2 Hðd; pÞ3 H, 3 Hðd; nÞ4 He, 3 Hða; gÞ7 Li, 3 Heðd; pÞ4 He, 3 Heðn; pÞ3 H, 3 Heða; gÞ7 Be, 7 Liðp; aÞ4 He and 7 Beðn; pÞ7 Li, cross-sections have been measured in the laboratory at the relevant energies. All experimental data have been compiled and analyzed in the framework of R-matrix theory for interpolation or extrapolation. In addition to providing more reliable recommended rates, the rate uncertainties have been evaluated on statistical grounds [17], providing upper and lower limits.

5. BBN primordial abundances compared to observations Fig. 7 shows the evolutions of the abundances (in mass fraction) as a function of time at the WMAP baryonic density. Neutrons are mostly captured to form 4 He while D and 3 He reach final values of  105 . After a sharp rise, 7 Li is efficiently depleted by the 7 Liðp; aÞ4 He reaction. At this density, 7 Li is produced through the formation of 7 Be via the 3 Heða; gÞ7 Be reaction. It will later decay to 7 Li. 7 Be destruction occurs through the 7 Beðn; pÞ7 Liðp; aÞ4 He channel which is limited by the scarcity of neutrons. At lower baryonic density more neutrons would survive but the 7 Liðp; aÞ4 He destruction mechanism would be less effective and 7 Li would be produced directly via the 3 Hða; gÞ7 Li reaction (Fig. 5). Fig. 8 shows the abundances of 4 He (mass fraction), D, 3 He and 7 Li (in number of atoms relative to H) as a function of the baryonic density. The ‘‘U’’ shape of the 7 Li abundance curve comes from the two modes of 7 Li synthesis discussed above and shown in Fig. 5. The thickness of the curves reflect the nuclear uncertainties. They

M1/(M1+E1)

0.8 0.6 0.4 0.2

10-2

10-1

1

10

ECM (MeV) Fig. 6. Theoretical n þ p-D þ g cross-sections [16] (solid lines) compared to experiments [18]: total cross-section (upper panel), absolute (middle panel) and relative (lower panel) M 1 component. The hatched area represents the Boltzmann factor at a typical temperature (arbitrary units) and the dashed line is its product with the total cross-section.

were obtained [19] by a Monte-Carlo calculation using for the nuclear rate uncertainties those obtained by Ref. [17]. The horizontal lines represent the limits on the 4 He,D and 7 Li primordial abundances deduced from observations as discussed in Section 3. The vertical stripe represents the baryonic density deduced from CMB observations by [3]. As shown in Fig. 8, the primordial abundances deduced either by BBN at CMB deduced baryonic density or from observations are in perfect agreement for deuterium. Considering the large uncertainty associated with 4 He observations, the agreement with CMBþBBN is fair. The calculated 3 He value is close to its galactic value showing that its abundance has little changed during galactic chemical evolution. On the contrary, the 7 Li, CMBþBBN, calculated abundance is significantly higher (a factor of  3) than the primordial abundance deduced in Ref. [6]. The origin of this discrepancy between CMB þ BBN and spectroscopic observations remains an open question. Indeed, it seems surprising that the major discrepancy affects 7 Li since it could a priori lead to a more reliable primordial value than deuterium, because of much higher observational statistics and an easier extrapolation to primordial values (Fig. 2). There are many tentative solution to this problem (nuclear, observational, stellar, cosmological, etc.) but none has provided yet a fully satisfactory solution. The derivation of the lithium abundance in

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1

WMAP

η = ηWMAP 1H

10-1

0.26

4He

n

4He

10-2

0.25 2H

10-4 10-5

3H

10-6

3He

0.24 0.23

-7

10

0.22

10-8 10-9

7Li

10-10

D/H

Mass fraction

Mass fraction

10-3

7Be

3He/H,

10-11 10-12 10-13

D

10-4

10-5

3He

10-14 102

103

104

10-6

Time (s) Fig. 7. Evolution of the abundances as a function of time at WMAP baryonic density. 7Li/H

halo stars with the high precision needed is difficult and requires a fine knowledge of the physics of stellar atmosphere (effective temperature scale, population of different ionization states, deviation from local thermodynamic equilibrium and 1D=3D model atmospheres). There is no lack of phenomena to modify the surface abundance of lithium: nuclear burning, rotational induced mixing, atomic diffusion, turbulent mixing, mass loss, etc. However, the flatness of the plateau over three decades in metallicity and the relatively small dispersion of data represent a real challenge to stellar modeling. In the nuclear sector, large systematic errors on the 12 main nuclear cross-sections are excluded [17,19]. Since the CMB results point toward the high Z region, a peculiar attention should be paid to 7 Be nucleosynthesis. However, there is no indication that a more efficient 7 Be nuclear destruction mechanism would be at work.

7Li

10-9

10-10 WMAP

10

1

10 η×1010

Fig. 8. Abundances of 4 He (mass fraction),D, 3 He and 7 Li (by number relative to H) as a function of the baryon over photon ratio Z (or Ob  h2 ) showing the effect of nuclear uncertainties.

Table 2 Abundance sensitivity: @logY=@logx.

6. Neutrons in BBN Neutrons play a major role in BBN as their abundance at freezeout determine the abundance of 4 He the n þ p-D þ g reaction is the starting point of nucleosynthesis and its late time abundance affects the 7 Li final abundance. Freezeout occurs when the weak rate Gn2p T 5 maintaining equilibrium becomes slower than the expansion rate HT 2 (Eq. (7)). Changes in Gn2p or HðT  1010 KÞ will hence affect the 4 He abundance. As the weak interaction rates are normalized to the neutron lifetime, the 4 He yield depends directly on tn . The sensitivity of calculated abundances (Yi with i ¼ 4 He; D; 3 He and 7 He) to change (as a constant factor) in various parameters (x ¼ tn , H, nðp; gÞd rate) are presented in Table 2: DYi =Yi versus Dx=x. These values were obtained by a fit of DYi =Yi for Dx=x ¼ 710% variations as within these limits, a linear dependence is a very good approximation. For instance, one reads DYp =Yp ¼ 0:73Dtn =tn . One can hence deduce from Fig. 4 that the precision of the neutron lifetime measurements is sufficient for BBN applications unless unexpected progress is made in 4 He observations. The influence on the other isotopes,

Isotope

tn

4

0.7325

0.7140

0.005

3

He

0.4192 0.1473

1.9336 0.6837

0.2228 0.088

7

Li

0.3998

1.5704

1.4379

He D

H

nðp; gÞd

when compared to the precision of their primordial abundance determinations, is even weaker. Table 2 also shows that, as expected, the effect of a tn variation on 4 He is almost degenerate with a change in the rate of expansion H. On the contrary, the influence of the nðp; gÞd rate is unexpected. The 7 Li final abundance depends strongly on the rate of this first reaction to take place after freezeout while other isotopes are little affected. A change by  30% of this rate would be sufficient to reconcile the observed and calculated 7 Li abundances. Fig. 6 displays the nðp; gÞd theoretical, total cross-section, and its M1 absolute and relative contributions compared with experimental data points. The product (dashed line) of the

ARTICLE IN PRESS

7. BBN as a probe of the early Universe

1

10 102 103 104 105 106 107 108 109 1010 1011 1012 1+z

Δα /α = 2x10-5 10-2

WMAP

Fig. 9. Typical evolution of the scalar field as a function of redshift in the context of a tensor-scalar theory of gravity showing attraction towards GR (see text). Dashed line and hatched area show when weak interaction freezeout and nucleosynthesis take place.

0.26

ΩBh2

4He

Mass fraction

0.25 0.24 0.23

3He/H,

D/H

0.22 10-3

D

10-4

10-5 3He

10-6 7Li

10-9 7Li/H

Now that the baryonic density of the Universe has been deduced from the observations of the anisotropies of the CMB radiation with a precision that cannot be matched by BBN, one may wonder whether primordial nucleosynthesis studies are still useful. In the Report by the ESA-ESO Working Group on Fundamental Cosmology [20] it is shown that two of the most important issues in cosmology are modified gravity and varying constants. We will present shortly two examples of BBN studies that can help constrain these models and mention a few other topics of importance to particle physics. The CMB radiation that is observed was emitted when the Universe became transparent  3  105 years after the Big-Bang. On the contrary, the freezeout of weak interactions between neutrons and protons, and BBN, occurred at a fraction of a second, and a few minutes after the Big-Bang. With the exception of the baryonic density, BBN parameters have all been determined by laboratory measurements. Comparison between light element observed and calculated abundances can hence be used to put constraints on the physics prevailing in the first seconds or minutes of the Universe. Table 2 shows that a 10% change in the expansion rate is sufficient to drive the 4 He and D abundances out of the observational limits. 4 He yield is sensitive to the expansion rate at the time of n=p freezeout, i.e. at around 1010 K and 0.1–1 s after the Big-Bang, while the other isotopes are sensitive to its value 3– 20 min after. Hence, the 4 He abundance is of particular interest as it depends essentially on two quantities: the expansion and the weak reaction rates that can both be precisely obtained from theory. There are many potential sources of deviations from the nominal expansion rate HðtÞ. The geff factor (Eq. (7)) could be higher if yet unknown relativistic particles were present. Indeed, before the LEP experiments, 4 He in BBN was used to constrain the number of light neutrino families [21]. It should be noted that the spin factor g of other hypothetical light particles is not sufficient to calculate geff as their cross-section for interaction with ordinary particles is needed to calculate their temperature at BBN time. For instance, the neutrino temperature is smaller than the photon temperature because they decouple before electron–positron annihilation. More weakly interacting particles would decouple even earlier, have a lower temperature and hence contribute less to geff . Gravity could differ from its general relativistic description. For instance a scalar field, in addition to the tensor field of general relativity (GR), appears naturally in superstring theories. As an example (Fig. 9), theories with a quadratic coupling of the scalar field with matter, are attracted towards GR [22]. Constraints from today (at z ¼ 0 from celestial mechanics) and CMB (at z  1000) can be supplemented by BBN (Fig. 9) at redshifts of 3  107 ozo3  108 and z  3  109 (weak interactions freezeout). The effect of the scalar field on BBN is to modify the rate of expansion as long as it is of the order of the usual tensor component (i.e. f1 in Fig. 9). In this context, the evolution of the scalar field is driven by the presence of non-relativistic matter, i.e. when electron–positron annihilation takes place and in the matter

102 1 10-2 10-4 10-6 10-8 10-10 10-12 10-14 10-16 10-18 10-20

229

10-10 1

WMAP

Boltzmann factor (hatched area) and the total cross-section peaks at  25 keV. This is hence the energy important for BBN and experimental data rule out a possible  30% change from the theoretical rate used in BBN. (We will see below that this may however have taken place in the early Universe.) This unexpected effect can be traced to the increased neutron abundance at 7 Be formation time for a high nðp; gÞd rate making its destruction by neutron capture, 7 Beðn; pÞ7 Liðp; aÞ4 He, more effective.

φ2

A. Coc / Nuclear Instruments and Methods in Physics Research A 611 (2009) 224–230

10 η×1010

Fig. 10. Solid lines: same as Fig. 8 but neglecting nuclear uncertainties. Dashed lines: an example of the effect of varying constants within a model (see text).

dominated era. Constraints from BBN [23] can then put limits on the parameters (initial scalar field value, attraction strength towards GR, etc.).

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There are conflicting results [24,25] concerning the variation of the fine structure constant ðDaem =aem 106 Þ as observed in cosmological clouds ð0:4ozo2:3Þ on the line of sight of quasars. It would induce changes in the wavelengths corresponding to some observable atomic transitions. Coupled variation of the fundamental coupling constants is also motivated by superstring theories (see Ref. [26] for a review). Hence, a variation of aem should induce variations of the masses of the particles, the energy scale of the strong interaction, LQCD , the Fermi constant of the weak interactions, etc. The impact of these variations on the nuclear reaction rates is very difficult to estimate, as in general, nuclear physics uses phenomenological models whose parameters are not explicitly linked to fundamental constants. However, it is possible to estimate the variation of Qnp , tn , BD (binding energy of deuterium) and consequently the variation of the weak and nðp; gÞd rates. In particular, a relatively small ð 4%Þ change of BD at BBN epoch would induce a larger variation [8] of the nðp; gÞd reaction rate sufficient to reconcile all primordial abundances deduced from observations with BBN calculations. This is what is shown in Fig. 10 for Daem =aem ¼ 2  105, typical values for the other parameters, and the corresponding induced changes in me , mn , mp , Qnp , tn and BD (see details in Ref. [27]). Here, in this illustration, the other reaction rates are assumed to be unaffected or to have a negligible effect. This is certainly true for 4 He as it is governed by the weak rates only. Further investigations are underway to estimate the variations induced on the other rates [28,29] and may confirm the effect on the 7 Li abundance.

8. Conclusions The baryonic density of the Universe as determined by the analysis of the CMB anisotropies is in very good agreement with Standard BBN compared to D primordial abundance deduced from cosmological cloud observations. However, it disagrees with lithium observations in halo stars (Spite plateau). Presently, the most favored explanation is lithium stellar depletion but investigations of other solutions continue. Nevertheless, primordial nucleosynthesis remains an invaluable tool for probing the physics of the early Universe. When we look back in time, it is the ultimate process for which we a priori know all the physics involved. Hence, departure from its predictions provide hints for new physics or astrophysics. Besides the few examples given above, many particle physics issues can also be constrained by BBN like for instance non-standard neutrino properties (degeneracy, sterile neutrinos) [30], nuclear reactions catalysis by charged heavy relic particles [31,32], to name just a few.

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